An interior angle of a regular convex polygon is 162(degrees). Find the number of sides.
So the exterior angle = 180-162 = 18°
sum of exterior angles = 360°
so 18n = 360
n = 20
It is a 20-gon
or, using interior angles,
180(n-2) = 162n
180n-360 = 162n
18n = 360
n = 20
http://www.mathsisfun.com/geometry/polygons.html
To find the number of sides in a regular convex polygon when given the measure of an interior angle, we can use the formula:
Number of sides = 360 degrees / measure of each interior angle
In this case, we are given that the measure of each interior angle is 162 degrees. Plugging this value into the formula:
Number of sides = 360 degrees / 162 degrees
Simplifying this expression:
Number of sides = 2.222...
We need to round this decimal to the nearest whole number, as the number of sides in a polygon must be a whole number. Since you cannot have a fraction of a side, we need to consider the nearest whole number that is either less than or equal to 2.222.
Therefore, the number of sides in the polygon is 2.
However, it is important to note that a polygon with 2 sides is not possible. A polygon must have at least 3 sides to be considered as such. Therefore, it is likely that there is an error in the question or the information provided.
If we assume that the given measure of 162 degrees is correct, we can conclude that the polygon in question does not exist.